What are the odds?

Stuff (from the Sydney Morning Herald) reports that a baby was born at exact 2:22 and 22 seconds on February 22nd. An Australian maths professor is quoted as saying

“It’s about 1 in 30 million is the chance of being born at that precise second,”

Maths nerds will recognise that as the number of seconds in a year (roughly π times ten million), and music nerds will remember 525,600 as the number of  minutes in a year and multiply by 60.  So, 1 in 30 million is the chance of picking a particular second if you pick one randomly from a year. It seems a bit strange to give that as the answer for the baby’s chance of being born at that precise time.

If you had picked this specific baby, Bodhi, in advance, his chance of being born at a particular second depends on how much variation there is in birth times.  They’re roughly a Normal distribution with a standard deviation of 16 days, and it turns out this gives a chance of about 2.5% of being born five days early and so about one in 3.6 million of being born in a particular second on that fifth day early.

But we didn’t pick this specific baby in advance and look at when he was born. We picked the time and looked for the baby. There are nearly 300,000 births per year in Australia; about one per 100 seconds.  There would be about a 1 in 100 chance that some baby in Australia is born at one particular second.

So far we’ve been saying there’s one particular second. But the baby was born at 14:22:22 and presumably 02:22:22 would have done just as well. Or maybe 22:02:22 or 22:22:22.  It’s not really one special second in the day.  And on top of that, a baby isn’t really born at a single second — there’s at least a small amount of flexibility in how you define the time, and you know someone is going to take advantage of the flexibility.  What would be really surprising would be a birth recorded as 2:22:19pm on 22/2/2022.